If hx - min x-x2 for x - R- Find LHD and RHD at x - 1-

(A) Let plot the graph of f(x) = x and f(x) = x2 Taking min of x2, x we get LHD ⇒ → 0^ limf(x+ x).f(x)/ x where f(x) = x^2 at x = 1 ⇒ → 0^ lim f(x+ x)^ ...

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Byju's Answer

Standard XIII

Mathematics

Relation between Continuity and Differentiability

If hx = min x...

Question

If h(x) = min {x,x²} for x ϵ R. Find LHD and RHD at x = 1.

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Solution

(A) Let plot the graph of f(x) = x and f(x) = x²

Taking min of x², x we get

LHD $\Rightarrow l i m △ \to 0^{-} \frac{f (x + △ x) . f (x)}{△ x} w h e r e f (x) = x^{2} a t x = 1$
$\Rightarrow l i m △ \to 0^{-} \frac{f (x + △ x)^{2} - x^{2}}{△ x} = l i m △ \to 0^{-} \frac{2 △ x . x + △ x^{2} - x^{2}}{△ x} = l i m △ \to 0^{-} 2 x + △ x$
$R H D △ l i m △ \to 0^{+} \frac{(x + △ x) - (x)}{△ x} = l i m △ \to 0^{+} \frac{△ x}{△ x} = 1$
$∴$ LHD = 2, RHD = 1

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If h(x) = min {x,x2} for x ϵ R. Find LHD and RHD at x = 1.

If h(x) = min {x,x²} for x ϵ R. Find LHD and RHD at x = 1.